Networking is simply putting youself, and what you want, out there. It means that at whatever club, church social, or sporting event you attend, you mention that you are looking for a career change. This doesn't mean that it is all that you talk about with your friends and family, but it does mean that you add your career change to your list of things that you discuss with people you meet.
Let me show you how this works. Let's say that you're volunteering at a bake sale for your child's school. You spend a good portion of the day helping out, and end up working the cash register with a person you haven't really talked to before. During the course of the day, it is appropriate for you to mention that you're looking for a new job. You should also give them some details about the types of work you enjoy doing (i.e. are you a people-person, are you very technically savvy, etc), and even some of the companies you're interested in working for. There's no need to go on for hours, but you want to give them a clear enough picture of what you are looking for to make it easy for them to flip through their mental rolodex and think of someone who could help you. If you're lucky, your new friend could turn to you and say "Did you know that the guy over there works at Company XYZ? He's a good friend of mine, I'll introduce you." This may not pay off in all cases, but more times than not they will know someone who could help you, or could take your card and call you later if they think of anyone. At least you have solicited their help in some way, it could pay off, it could not, but the rewards far outweigh the chance of not getting a lead.
People enjoy helping other people, but they are unable to do this unless you ask for their help. Networking this way is simply a way of making a connection with others to let them know what you are looking for.

